In a homogeneous and isotropic universe, in principle, the observations of luminosity distances to astronomical objects over the sky should not be directional. However, in fact, due to the matter inhomogeneities of the large-scale structure and the local motion of observer [1]}, there are tiny anisotropies leading to the appearance of correction term for the luminosity distance \(d_L\) , given by [2]}, [3]}, [4]}
\(d_{L}(z, \mathbf {n})&=&d_{L}^{(0)}(z)+d_{L}^{(1)}(z)\cos \theta , \\d_{L}^{(0)}(z) &\equiv & \frac{1}{4 \pi } \int d \mathbf {n} d_{L}(z, \mathbf {n}), \\d_{L}^{(1)}(z) &\equiv & \frac{3}{4 \pi } \int d \mathbf {n}(\mathbf {n} \cdot \mathbf {e}) d_{L}(z, \mathbf {n}),\) 
